Final answer:
To find the probability that the sample proportion is more than 22%, calculate the standard error of the sample proportion using the formula SE = sqrt((p*(1-p))/n), where p is the known proportion and n is the sample size. Then calculate the z-score using the formula z = (sample proportion - population proportion) / standard error. Finally, use the z-score to find the probability using the standard normal distribution table or a calculator.
Step-by-step explanation:
To find the probability that the sample proportion is more than 22%, we first need to calculate the standard error of the sample proportion. The formula for the standard error is:
SE = sqrt((p*(1-p))/n)
where p is the known proportion of people riding public transport without paying, and n is the sample size.
In this case, p = 0.19 and n = 75. Plugging these values into the formula, we get:
SE = sqrt((0.19 * (1 - 0.19)) / 75) ≈ 0.0435
Next, we can calculate the z-score using the sample proportion of 22%:
z = (sample proportion - population proportion) / standard error
Plugging in the values, we get:
z = (0.22 - 0.19) / 0.0435 ≈ 0.6897
Finally, we can use the z-score to find the probability using the standard normal distribution table or a calculator. The probability that the sample proportion is more than 22% is equal to 1 minus the probability of the z-score. Depending on the specific table or calculator you are using, you can look up the probability and subtract it from 1 to find the final answer.